Dielectric susceptibility anisotropy

To study the N-1 phase transition, it is necessary to find some physical property proportional to 5(7) that can be measured accurately as a function of temperature. There are many possibilities, which include depolarization of Raman spectra, diamagnetic susceptibility anisotropy, NMR deuterium quadrupole splitting, dielectric constant... 

Aj (extracted from measurements along and normal to the nematic director), is proportional to the nematic order parameter S. The proportionality constant is the anisotropy of the corresponding molecular attribute (Aj - A ). When the longitudinal and transverse molecular attributes and At. respectively, are accessible, the nematic order parameter and its temperature dependence may be determined. Properties such as the molar refractivity, polarizability, magnetic (dielectric) susceptibility, etc., are typical quantities that have been studied to infer the nematic order parameter. 

The basis of the majority of specific liquid crystal electrooptical effects is found in the reorientation of the director (the axis of preferred orientation of the molecules) in the macroscopic volume of the material under the influence of an externally applied field or the fiow of the liquid. Anisotropy of the electrical properties of the medium (of the dielectric susceptibility and the electrical conductivity) is the origin for reorientation, whereas the dynamics of the process also depend on the viscoelastic properties and the initial orientation of the director of the mesophase relative to the field. The optical properties of the medium, its local optical anisotropy, are changed as a result of this reorientation of the director (either occurring locally or throughout the whole of the sample) and underlies all the known electrooptical effects. 

The Frederiks transition induced by an electric field has certain specific features not observed in the magnetic field equivalent. First, as the dielectric anisotropy is usually much higher than the magnetic one, the distortion leads to a spatial dependence of the dielectric susceptibility and a certain inhomogeneity in the electric field. Secondly, the character of the distortion may be affected by the electric conductivity and the influence of the flexoelectric effect. A discussion of these effects may be found in literature (e.g. [8, 9]). 

Kochergin et al. 2004, 2005 Ruda and Shik 2011) and is basically understood. Consistently the Structural anisotropy of (110) porous Si also affects the dielectric properties in general, like the optical absorption coefficient and nonlinear susceptibility (Zabotnov et al. 2005 Timoshenko et al. 2003 Soboleva et al. 2005 Efimova et al. 2007a, b). 

The results are reproduced in Fig. 2.6 [15]. It can be seen that with a drop in temperature the difference e, — e decreases even in the nematic phase. The change in sign of the anisotropy of the molar susceptibility occurs either in the smectic A phase (homologues with n = 7 and 8) or in the nematic phase (n = 6) near the transition point to smectic A. The dielectric anisotropy decreases both because of the decrease in s, and the increase in e . The effect clearly indicates the presence of the short-range smectic order even in the nematic phase. The decrease in and the increase in e , due to the short-range smectic order in the nematic phase (and the long-range order in smectic A), occurs as a consequence of correlation in... 

An advantage with respect to the methods discussed in Sect. 4.1.1 is that a homogeneous or homeotropic orientation of the mesogens can be chosen independently of the chain conformation. For the orientation in an electric or magnetic field it has to be considered that the mesogens must have a suitable anisotropy of the dielectric constant and the diamagnetic susceptibility, respectively. 

Here Xa = X - Xx and 6a = e - Sx are the relative diamagnetic and dielectric anisotropies, so that the uniaxial susceptibility and dielectric tensors can be written in Cartesian coordinates in the form... 

In general, when an external field is applied to a nonpolar or polar liquid crystal, a quadratic- or linear-in-field term, respectively, must be added to the expression for the free energy density of the medium. The quadratic-in-field energy terms describe the interaction of the electric or magnetic field with the dielectric or diamagnetic anisotropy of susceptibility ... 

Reorientation of director L (or the optical axis) of the macroscopic volume of a liquid crystal under the effect of a field or flow of a liquid is Ae basis of most of the Imown electro- and magneto-optical effects. The anisotropy of the electrical and magnetic properties of the medium (dielectric constant Ae, diamagnetic susceptibility A%, electrical conductivity Aa) is the direct cause of orientation. The rearrangement processes are a function of the initial mientation of the molecules of the liquid crystal and its viscoelastic properties. The change in the c tical properties as a result of reorientation is the consequence of the optical anisotropy of liquid crystals. 

The order parameters defined previously in terms of the directional averages can be translated into expressions in terms of the anisotropies in the physical parameters such as magnetic, electric, and optical susceptibilities. For example, in terms of the optical dielectric anisotropies Ae = one can define a so-called macroscopic order parameter which characterizes the bulk response... 

If the pitch of the cholesteric is not changed by an external probing field (electric, magnetic, or optical), the physical properties of cholesterics are those of localty rmiaxial crystals. In other words, the anisotropies in the dielectric constant (Ae = ey - Sj ), electric conductivity (Aa = ay CTj ), magnetic susceptibility (A% = - % ), and so... 

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